2017
Том 69
№ 7

All Issues

On the Relationship Between the Rate of Polynomial Approximation of an Entire Function and its Order and Type

Dveirin M. Z.


Abstract

We study the relationship between the order and type of an entire function and the rate of its best polynomial approximation for various Banach spaces of functions analytic in the unit disk. The relations specifying the order and type of the entire function via the sequence of its best approximations are deduced. The results are obtained by generalizing the results obtained earlier by Reddy, Ibragimov, Shyhaliev, Vakarchyk, and Mamadov.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 10, pp 1498-1514.

Citation Example: Dveirin M. Z. On the Relationship Between the Rate of Polynomial Approximation of an Entire Function and its Order and Type // Ukr. Mat. Zh. - 2015. - 67, № 10. - pp. 1333-1347.